Heretofore, precision polishing has been performed using a polishing liquid on surfaces of materials such as metals, metalloids, non-metals and their oxides. For instance, the surface of a silicon wafer used as a component of a semiconductor device, etc., is generally polished to a high quality mirror finish via a lapping step (rough polishing step) and a polishing step (precision polishing step). The polishing step typically comprises a first polishing step and a final polishing step. Patent Documents 1 and 2 are cited as technical literatures related to polishing compositions used primarily for polishing semiconductor substrates such as silicon wafers, etc.